# Prime factorization of $3196$

The calculator will find the prime factorization of $3196$, with steps shown.

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Find the prime factorization of $3196$.

### Solution

Start with the number $2$.

Determine whether $3196$ is divisible by $2$.

It is divisible, thus, divide $3196$ by ${\color{green}2}$: $\frac{3196}{2} = {\color{red}1598}$.

Determine whether $1598$ is divisible by $2$.

It is divisible, thus, divide $1598$ by ${\color{green}2}$: $\frac{1598}{2} = {\color{red}799}$.

Determine whether $799$ is divisible by $2$.

Since it is not divisible, move to the next prime number.

The next prime number is $3$.

Determine whether $799$ is divisible by $3$.

Since it is not divisible, move to the next prime number.

The next prime number is $5$.

Determine whether $799$ is divisible by $5$.

Since it is not divisible, move to the next prime number.

The next prime number is $7$.

Determine whether $799$ is divisible by $7$.

Since it is not divisible, move to the next prime number.

The next prime number is $11$.

Determine whether $799$ is divisible by $11$.

Since it is not divisible, move to the next prime number.

The next prime number is $13$.

Determine whether $799$ is divisible by $13$.

Since it is not divisible, move to the next prime number.

The next prime number is $17$.

Determine whether $799$ is divisible by $17$.

It is divisible, thus, divide $799$ by ${\color{green}17}$: $\frac{799}{17} = {\color{red}47}$.

The prime number ${\color{green}47}$ has no other factors then $1$ and ${\color{green}47}$: $\frac{47}{47} = {\color{red}1}$.

Since we have obtained $1$, we are done.

Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $3196 = 2^{2} \cdot 17 \cdot 47$.

The prime factorization is $3196 = 2^{2} \cdot 17 \cdot 47$A.